Czechoslovak Mathematical Journal, Vol. 67, No. 3, pp. 827-837, 2017
On decomposability of finite groups
Ruifang Chen, Xianhe Zhao
Received April 21, 2016. First published March 2, 2017.
Abstract: Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$-conjugacy classes, and it is called $n$-decomposable in $G$ if it is a union of $n$ distinct $G$-conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained in its non-trivial normal subgroups are 2, 3, 4 and 5.
Keywords: non-perfect group; $G$-conjugacy class; $n$-decomposable group
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Affiliations: Ruifang Chen (corresponding author), Xianhe Zhao, School of Mathematics and Information Science, Henan Normal University, No. 46, East of Construction Road, Xinxiang 453007, Henan, P. R. China, e-mail: firstname.lastname@example.org, email@example.com